# Calculation of a comet orbiting Sun

• MelkoRR
In summary: Apogee" should be "aphelion" or "apoapsis".In summary, the problem involves finding the time that a comet, orbiting the sun in a parabolic orbit, spends closer to the sun than the Earth within the Earth's orbit. This requires using the Parabolic Eccentric Anomaly and treating the Earth's orbit as circular.
MelkoRR

## Homework Statement

a comet is orbiting around the Sun in a parabolic orbit . center of the sun to perigee of the comet's orbit distance is 58 km .
find the time required for the comet to transit into the Earth orbit around the sun .

## The Attempt at a Solution

no clue

i think this problem is better off in the advanced section !

MelkoRR said:
i think this problem is better off in the advanced section !
Done!

Can you clarify the phrase: "find the time required for the comet to transit into the Earth orbit around the sun "? Transit from where? You need to specify the portion of the orbit involved.

Do you mean the time spent by the comet closer to the Sun than the Earth (within the orbit of the Earth)?

By the way, the quoted material is not correct when it states that the is no "eccentric anomaly" for the parabola. There is what is called the Parabolic Eccentric Anomaly, often denoted by D where

##D = \sqrt{p}~tan~\frac{\nu}{2}##

See, for example, "Fundamentals of Astrodynamics" by Bate, Mueller, and White, chapter 4.

MelkoRR said:

## Homework Statement

a comet is orbiting around the Sun in a parabolic orbit . center of the sun to perigee of the comet's orbit distance is 58 km .

You realize, of course, that at this perigee distance of 58 km from the sun's center, the comet is traveling thru the sun?!?

This thread was reported to the Mentors because you showed zero effort. But a Mentor and a retired Mentor are posting in the thread, so they will handle this.

SteamKing said:
You realize, of course, that at this perigee distance of 58 km from the sun's center, the comet is traveling thru the sun?!?

my bad , it's 58 million kilometers !

gneill said:
Done!

Can you clarify the phrase: "find the time required for the comet to transit into the Earth orbit around the sun "? Transit from where? You need to specify the portion of the orbit involved.

Do you mean the time spent by the comet closer to the Sun than the Earth (within the orbit of the Earth)?

By the way, the quoted material is not correct when it states that the is no "eccentric anomaly" for the parabola. There is what is called the Parabolic Eccentric Anomaly, often denoted by D where

##D = \sqrt{p}~tan~\frac{\nu}{2}##

See, for example, "Fundamentals of Astrodynamics" by Bate, Mueller, and White, chapter 4.
the problem is i don't quite understand the problem , and I've translated the problem form Persian to English . another translation that could be told is :

A comet is orbiting around the Sun in a parabolic orbit . Assuming the distance between the center of the sun to perigee of the comet's orbit is 58 million km, find the duration the comet spends in Earth's orbit.

I think the best question before any attempt for solving the problem is : "Can a comet, while staying in it's own orbit, spent some time on Earth's orbit around the sun?"

MelkoRR said:
the problem is i don't quite understand the problem , and I've translated the problem form Persian to English . another translation that could be told is :

A comet is orbiting around the Sun in a parabolic orbit . Assuming the distance between the center of the sun to perigee of the comet's orbit is 58 million km, find the duration the comet spends in Earth's orbit.
Change "in" to "within" then I would agree with this interpretation. That is, find the time that the comet spends closer to the Sun that the Earth.
I think the best question before any attempt for solving the problem is : "Can a comet, while staying in it's own orbit, spent some time on Earth's orbit around the sun?"
Earth's orbit is an ellipse while the comet's is parabolic. They are different geometrical shapes that won't coincide for any length of time. The best that can happen is an intersect (crossing), which would happen in an instant of time.

gneill said:
Earth's orbit is an ellipse while the comet's is parabolic. They are different geometrical shapes that won't coincide for any length of time. The best that can happen is an intersect (crossing), which would happen in an instant of time.

exactly this is my thought , it would be a point , but the problem is asking for duration !

gneill said:
Change "in" to "within" then I would agree with this interpretation. That is, find the time that the comet spends closer to the Sun that the Earth.

so how could we find the time ?!

would it be possible for the comet to spend some time in Earth's orbit around sun in this case ?

MelkoRR said:
exactly this is my thought , it would be a point , but the problem is asking for duration !
so how could we find the time ?!
Well, that's what you need to work out. We can't hand you an answer here. You have to do some research and show an attempt.

I did provide a hint for a starting point: The Parabolic Eccentric Anomaly.

gneill said:
Well, that's what you need to work out. We can't hand you an answer here. You have to do some research and show an attempt.

I did provide a hint for a starting point: The Parabolic Eccentric Anomaly.
Thank you , i will post my progress here as soon as i reached somewhere !

MelkoRR said:
would it be possible for the comet to spend some time in Earth's orbit around sun in this case ?
Again, it depends on your definition of "in". Clearly the image shows the comet's orbit spends a portion of its time within the Earth's orbit.

Note that the eccentricity of the Earth's orbit is very small so it's very close to circular. It's highly likely that you can treat it as circular for the purposes of this problem, otherwise they would have given you precise orbit details and timings to work with for both bodies.

By the way: "perigee" (the point closest to earth) should be "perihelion" (the point closest to sun) or "periapsis" (the closest point to the central object in general).

## 1. How do scientists calculate the orbit of a comet around the Sun?

Scientists use mathematical equations and data collected from observations to calculate the orbit of a comet. They take into account factors such as the comet's mass, velocity, and distance from the Sun to determine its orbit.

## 2. What tools or methods are used to calculate the orbit of a comet?

Scientists use a variety of tools and methods to calculate the orbit of a comet. These include telescopes, radar observations, and computer simulations. They also use data from previous comet sightings and historical records to help with their calculations.

## 3. How accurate are the calculations of a comet's orbit?

The accuracy of the calculations depends on the quality and quantity of data available. If scientists have a lot of precise data, their calculations can be very accurate. However, there are always some uncertainties and variables that can affect the accuracy of the calculated orbit.

## 4. What factors can influence the orbit of a comet?

The orbit of a comet can be influenced by several factors, including the gravitational pull of other objects in the solar system, such as planets or other comets. The shape and composition of the comet can also affect its orbit, as well as any external forces, such as solar wind or collisions with other objects.

## 5. Can the orbit of a comet change over time?

Yes, the orbit of a comet can change over time due to various factors, such as gravitational interactions with other objects, or the comet losing mass as it travels closer to the Sun. These changes can be observed and calculated by scientists using data collected over time.

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